Let/. It :0 ---0 G be any two self maps of a compact connected oriented Lie group G. In this paper, for each positive integer k , we associate an integer with fk,hi . We relate this number with Lefschetz coincidence number. We deduce that for any two differentiable maps f, there exists a positive integer k such that k 5.2+1 , and there is a point x C G such that ft (x) = (x) , where A is the rank of G . Introduction Let G be an n-dimensional com -pact connected Lie group with multip-lication p ( .e 44:0 xG--+G such that p ( x , y) = x.y ) and unit e . Let [G, G] be the set of homotopy classes of maps G G . Given two maps f , f G ---• Jollowing [3], we write f. f 'to denote the map G-.Gdefined by 01.11® =A/WO= fiat® ,sea Given a point g EC and a differ-entiable map F: G G , write GA to denote the tangent space of G at g [4,p.10] , and denote by d x F the linear map rig F :Tx0 T, (x)G induced by F , it is called the differential of Fat g [4,p.22]. Let LA, Rx :0 G be respec-tively the left translation Lx(i)=4..(g,e) , and the right translation Rx(1)./..(gcg). Then there is a natural homomorphism Ad ,the adjoin representation, from G to GL(G•), (the group of nonsingular linear transformations of Qdefined as follows:- Ad(g)= deRe, od,Lx. Note that d xRc, ad.; =d(4,( Lx(e)))0 de; =d.(4, 04)=4(40 Re) = d(4(4, (e)))0 (44, =d ar, o (44, . Since G is connected , the image of Ad belongs to the connected component of G(G)containing the identity,i.e. for each g E 0, detAd(g) > 0 . By Exercise Al • Dr.-Prof.-Department of Mathematics- College of Science- University of Baghdad. •• Dr.-Department of Mathematics- College of Science for Woman- University of Baghdad.
The problem of multi assembly line balancing appears as one of the most prominent and complex type of problem. The research problem of this dissertation is concerned with choosing the suitable method that includes the nature of the processes of the multi assembly type of the sewing line at factory no. (7). The State Company for Leather Manufacturing. The sewing line currently suffers from idle times at work stations which resulted in low production levels that do not meet the production plans. The authors have devised a flexible simulation model which uses the uniform distribution to generate task time for each shoe type produced by the factory. The simulation of the multi assembly line was based on assigni
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Abstract
Electrical magnate was designed and constructed, the optimum Magnetic flux and the effect of time on the physical properties of the alkaline (magnetic water) produced from the bottled drinking water [the total dissolved solids (TDS) or the electrical conductivity, and pH] were studied, to simulate ZamZam water in Mekka Saudi Arabia. Also, the efficiency of magnetic field from this designed electrical magnate in decreasing the TDS of sea water (of 1500 ppm NaCl Content), to convert it to water suitable for irrigation (TDS<1000 ppm) was investigated in this work.The results show that the magnetic flux from our designed electrical magnate in the range of (0.013- 0.08) Tesla and 30 minut
... Show MoreThe research aimed to modeling a structural equation for tourist attraction factors in Asir Region. The research population is the people in the region, and a simple random sample of 332 individuals were selected. The factor analysis as a reliable statistical method in this phenomenon was used to modeling and testing the structural model of tourism, and analyzing the data by using SPSS and AMOS statistical computerized programs. The study reached a number of results, the most important of them are: the tourist attraction factors model consists of five factors which explain 69.3% of the total variance. These are: the provision of tourist services, social and historic factors, mountains, weather and natural parks. And the differenc
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In the present work, Response Surface Methodology (RSM) was utilized to optimize process variables and find the best circumstances for indirect electrochemical oxidation of mimicked wastewater to remove phenol contaminants using prepared ternary composite electrode. The electrodeposition process is used for the synthesis of a ternary composite electrode of Mn, Co, and Ni oxides. The selected concentrations of metal salts of these elements were 0.05, 0.1, and 1.5 M, with constant molar ratio, current density, and electrolysis time of 1:1:1, 25 mA/cm2, and 2 h. Interestedly, the gathered Mn-Co-Ni oxides were deposited at both the anode and cathode. X-ray diffraction (XRD) and scanning electron microscopy (SEM) facilitated the qualitative char
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Praise be to God, Lord of the worlds, and prayers and peace be upon our master Muhammad and upon his family and companions as a whole.
The topic of attention was drawn to the attention of the speakers, as it made me ponder it carefully, and my goal in that is to know the reason for the interest of the speakers and their care for it, and to clarify from their books the purpose of making this topic one of the advanced investigations with them.
The idea of writing a paper on the subject of consideration was not absent from my thinking, because I saw the attention of speakers on this issue, as they made it one of the first issues that they deal with studying in their work
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